The concept of a pseudo-complementation on a Generalized Almost Distributive Lattice (GADL) with 0 is introduced and proved that there is a one-to-one correspondence between the pseudo-complementations on a GADL L with 0 and left identity elements of L. The concept of *–GADL, disjunctive GADL is also introduced. We characterized *–GADL in terms of disjunctive GADL.

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Characterized Quasi-complemented Almost Distributive Lattice (ADL) in terms of dominator ideals. By using the closure operator on the set of all ideals of an ADL introduced the concept of closure ideals and studied their important results. Finally, the class of all closure ideals of ADL are isomorphic to the class of all ideals of [Formula: see text].

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